[Insert – Cover Page – Choose a template] Quantitative
Structure-Activity
Relationships as Prediction Tools
page break [Insert – Page Break] Contents [Calibri 28, Align = Left, Bold]
page break [Insert – Page Break] Abstract [Heading 1] - [Home – Style – Heading 1]
The Molecular Descriptors Family on the Structure-Property/Activity Relationships (MDF
SPR/SAR) is an area of computational research able to generate a family of molecular
descriptors and to build models in order to estimate and predict the property/activity of chemical
compounds. This review aims to briefly present the MDF SPR/SAR methodology and to discuss
its abilities to estimate and predict different properties and activities.
Introduction [Heading 1] - [Home – Style – Heading 1]
Structure-Activity Relationships (SARs), Structure-Property Relationships (SPRs) and PropertyActivity Relationships (PARs) were first introduced by Louis Pluck HAMMETT in 1937 [1]. A
more recent review summarizes the most important applications of Hammett’s equation [2].
The idea of linking the structure of a compound with its activity or property was published before
the introduction of the SAR concept. In 1868, Crum-Brown and Fraser noted that the activity of
a compound is a function of its chemical composition and structure [3]. In 1893, Richet and
Seancs demonstrated that cytotoxicity was inversely related with water solubility on a set of
organic compounds [4]. In 1899, Mayer demonstrated that the narcotic action of a sample of
organic compounds was related with solubility in olive oil [5]. Therefore, Hammett [6] and Taft
[7] could be said to have laid the basis of QSAR/QSPR development.
Quantitative relationships (QSAR, QSPR, QPAR), which are mathematical approaches to the
link between the structure and the property/activity of chemical compounds in a quantitative
manner [8], are applied when the property and/or activity are quantitative. Note that not all the
properties and activities of chemical compounds can be classified as quantitative. An example
could be the sweetness of sugar (one of the five basic tastes, being almost universally
perceived as a pleasurable experience), which can be appreciated only through comparison
(relative scale) since there is no single reference scale (such as the boiling and freezing point
and the Celsius scale for temperature). Properties that are expressed quantitatively may have
several reference scales. Consequently, the use of terms such as QSAR, QSPR, and QPAR is
currently avoided, the terms (Q)SAR, (Q)SPR, and (Q)PAR, or simply SAR, SPR, and PAR
being preferred.
As far as the structure is concerned, things are relatively simpler. Thus, an atom or a bond from
a molecule could exist (highlighted through electronic transitions and/or molecular vibrations
and/or rotations) or could not exist (0 or 1). Molecular geometry (especially the liquid or gas
phase) is more complicated. The Heisenberg principle (Werner HEISENBERG, 1901-1976, one
of the founders of quantum mechanics, a Nobel prize winner) demonstrates the rules of
uncertainty through the principles of uncertainty (molecular and atomic level) at micro level.
Moreover, molecular geometry depends on the environment on which a molecule is placed (the
vicinity of the molecule), the temperature, the pressure, etc. Thus, dealing with molecular
geometry is a matter of relativity if not a matter of uncertainty. In conclusion, in the field of
Structure-Property-Activity Relationships (SPARs) there are certainties (e.g. molecular
topology), uncertainties (e.g. molecular geometry), relativities (e.g. biological activities), and
evidences (e.g. physical-chemical properties).
Mathematical Chemistry [9], Quantum Chemistry [11], and Medicinal Chemistry [12] have
increasingly significant contributions to the design and improvement of drugs. The dynamics of
pharmaceuticals is high; new drugs appear on the market daily, even if the process is a longlasting one. Drug design has recently emerged as a new field [13]. The usage of computing
power was a major breakthrough.
The aim of the present paper is to present some models with abilities in prediction of a series of
chromatographic parameters and of hydrophobic/hydrophilic character.
Structure- Property/Activity Relationships: Models by Examples [Heading 1] - [Home –
Style – Heading 1]
SPR Models [Heading 2] - [Home – Style – Heading 2]
In order to justify the introduction of the molecular descriptors family on the structure-property
relationships the chromatogtaphic parameters on classes of compounds have been investigated
and are presented.
Chromatographic Parameters [Heading 3] - [Home – Style – Heading 3]
Polychlorinated Biphenyls - Relative Retention Time [Bold & Italic]
Sample size
MDF SPR Equation
SPR Determination (%)
MDF Descriptor(s): x1 & x2
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Property Scale
Model Statistics
Cross-Validation Leave-One-Out
206
ŷ=0.09·x-0.17
98
iIDRwHg
Hydrogen (H)
Space (geometry)
H2·d-1
Inversed
r=0.9921; s=0.02; F (p)=13013 (1.64·10-189)
rcv-loo=0.9920; scv-loo=0.02;
Fcv-loo (p)=12777 (1.06·10-188)
ŷ=0.02·x1-1.02·x2-5.99
99.7
ISDmsHt & lADrtHg
Hydrogen (H) & Hydrogen (H)
Bonds (topology) & Space (geometry)
H2·d-3 & H2·d-4
Identity & Logarithmic
r=0.9986; s=0.01; F (p)=36600 (1.10·10-265)
rcv-loo=0.9985; scv-loo=0.01;
Fcv-loo (p)=35416 (3.33·10-264)
The relative retention time of polychlorinated biphenyls proved to be of both topological and
geometrical nature, and was related with the number of directly bounded hydrogens (see the
model with two descriptors).
Polychlorinated Biphenyls - Relative Response Factor [Bold & Italic]
Sample size
MDF SPR Equation
SPR Determination (%)
MDF Descriptor(s): x1 & x2
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Property Scale
Model Statistics
Cross-Validation Leave-One-Out
209
ŷ=0.53·x-0.51
63
iHMdTHg
Hydrogen (H)
Space (geometry)
H2·d-4
Inversed
r=0.7929; s=0.22; F (p)=351 (1.67·10-46)
rcv-loo=0.7873; scv-loo=0.22;
Fcv-loo (p)=337 (2.02·10-45)
ŷ=-357.3·x1+2.16·x2 +5.08
69
imMrFHt & iHDdFHg
Hydrogen (H) & Hydrogen (H)
Bonds (topology) & Space (geometry)
H2·d-2 & H2·d-2
Inversed & Inversed
r=0.8324; s=0.20; F (p)=232 (9.59·10-54
rcv-loo=0.8258; scv-loo=0.20;
Fcv-loo (p)=221 (3.73·10-52)
The MDF SPR abilities to estimate and predict the relative response factor are not strong, the
SAR determination being lower than 70%. According to the model with two descriptors, the
relative response factor of the polychlorinated biphenyls is both of topological and geometrical
nature and it strongly depends on the number of directly bounded hydrogens.
Organophosphorus Herbicides - Retention Chromatography Index [Bold & Italic]
Sample size
MDF SPR Equation
SPR Determination (%)
MDF Descriptor(s): x1 & x2
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Property Scale
Model Statistics
Cross-Validation Leave-One-Out
10
ŷ=0.32·x-3.37
94
IBPdqHg
Hydrogen (H)
Space (geometry)
1/H√H
Logarithmic
r=0.9708; s=0.78; F (p)=131 (3.08·10-6)
rcv-loo=0.9563; scv-loo=0.95;
Fcv-loo (p)=85 (1.55·10-5)
ŷ=6.37·x1+0.06·x2-62.36
99.92
lSDmwMt & iHPDEQg
Mass (M) & Charge (Q)
Bonds (topology) & Space (geometry)
M2·d-1 & M·d-2
Logarithmic & Inversed
r=0.9996; s=0.10; F (p) = 4348 (1.47·10-11)
rcv-loo=0.9993; scv-loo=0.13;
Fcv-loo (p)=2344 (1.28·10-10)
The retention chromatography index of organophosphorus herbicides proved to be estimated
and predicted by using the MDF approach. The SPR determination was higher than 90%.
According to the model with two descriptors, the retention chromatography index is of
topological and geometrical nature and depends on relative atomic mass and partial charge.
SAR Models [Heading 2] - [Home – Style – Heading 2]
The abilities of the molecular descriptors family approach have been investigated on samples of
biological active compounds in order to investigate their hydrophobicity/hydrophilicity.
Hydrophobic vs. Hydrophilic Character [Heading 3] - [Home – Style – Heading 3]
The hydrophobic or hydrophilic character, which is an important property in protein structure
and protein-protein interactions, is one of the most studied properties of the amino acids. Many
hydrophobicity scales have already been reported (see below). The differences between scales
are significant: Janin [14] and Kyte & Doolittle [15] classified cysteine as the most hydrophobic
while Wolfenden et al. [16] or Rose et al. [17] did not. These differences could be explained by
the fundamentally different methods used for constructing the scale.
Fifteen Standard Amino Acids – Hydrophobicity [Bold & Italic]
The hydrophobicity on the Bumble, Hessa et al. and Kyte & Doolittle scales revealed to be of
geometrical nature and directly related with partial charge on the sample of fifteen standard
amino acids (see the table below). Excepting the Bumble scale, the MDF models obtained had
a determination coefficient higher than 90%.
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor(s)
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-One-Out
15
ŷ=-160·x-0.07
65
AbmrEQg
Charge (Q)
Space (geometry)
Q·d2
Proportional
r=0.8085; s=1.68;
F (p)=25 (2.64·10-4)
rcv-loo=0.7550; scv-loo=1.88;
Fcv-loo (p)=17 (1.21·10-3)
15
ŷ=8.5·x-0.58
90.5
iMDRoQg
Charge (Q)
Space (geometry)
Q-1
Inversed
r=0.9514; s=0.44;
F (p)=124 (5.05·10-8)
rcv-loo=0.9351; scv-loo=0.51;
Fcv-loo (p)=90 (3.26·10-7)
15
ŷ=-21·x+12
95
IGDROQg
Charge (Q)
Space (geometry)
Q
Proportional
r=0.9759; s=0.71;
F (p)=260 (5.66·10-10)
rcv-loo=0.9659; scv-loo=0.80;
Fcv-loo (p)=203 (2.57·10-9)
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
The sample of twenty standard amino acids used for the following MDF SAR models contains:
alanine (Ala), arginine (Arg), asparagine (Asn), aspartate (Asp), cysteine (Cys), glutamine (Gln),
glutamate (Glu), glycine (Gly), histidine (His), isoleucine (Ile), leucine (Leu), lysine (Lys),
methionine (Met), phenylalanine (Phe), proline (Pro), serine (Ser), threonine (Thr), tryptophan
(Trp), tyrosine (Tyr), and valine (Val).
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor(s): x1 & x2
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-One-Out
20
ŷ=0.39·x-1.23
44
amMRLQt
Charge (Q)
Bonds (topology)
Q·d
Inversed
r=0.6649; s=1.21;
F (p)=14 (1.38·10-3)
rcv-loo=0.5961; scv-loo=1.37;
Fcv-loo (p)=7 (1.44·10-2)
20
ŷ=-27.79·x+6.55
66
immRoQg
Charge (Q)
Space (geometry)
Q-1
Inversed
r=0.8163; s=2.19;
F (p)=6 (1.14·10-5)
rcv-loo=0.7740; scv-loo=2.41;
Fcv-loo (p) = 27 (6.50·10-5)
20
ŷ=-1.73·x-2.88
69
LmDROQg
Charge (Q)
Space (geometry)
Q
Logarithmic
r=0.8309; s=1.70;
F (p)=40 (5.70·10-6)
rcv-loo=0.7936; scv-loo=1.87;
Fcv-loo (p) = 30 (3.34·10-5)
Two out of three of the above presented models for hydrophobicity proved that the activity was
of geometrical nature and depended on the partial charge. None of the above models was
strong; the coefficient of determination was lower than 70%.
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-One-Out
20
ŷ=7.35·x-3.37
71
iBmrWQt
Charge (Q)
Bonds (topology)
Q2/d
Inversed
r=0.8434; s=0.48;
F (p)=44 (3.00·10-6)
rcv-loo=0.800; scv-loo=0.54;
Fcv-loo (p) = 32 (2.25·10-5)
20
ŷ=10.63·x-1.99
74
iMPRoQg
Charge (Q)
Space (geometry)
Q-1
Inversed
r=0.8608; s=1.01;
F (p)=52 (1.11·10-6)
rcv-loo=0.8288; scv-loo=1.11;
Fcv-loo (p) = 39 (6.49·10-6)
20
ŷ=-6.57·x+1.47
75
AmDROQg
Charge (Q)
Space (geometry)
Q
Absolute
r=0.8661; s=0.6;
F (p)=54 (1.15·10-8)
rcv-loo=0.8344; scv-loo=0.73;
Fcv-loo (p) = 41 (7.94·10-8)
The MDF SAR model for hydrophobicity on the Wimley & White scale is of topological nature
and depends on partial charge. The hydrophobicity models on the Hoop & Woods and Cowan &
Whittaker scales revealed to be of geometrical nature and depended on partial charge. The
coefficient of determination associated with the above presented models proved not to be
powerful, even if the values were higher than 50%.
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
Sample size
MDF SAR Equation
20
ŷ=23.43·x+14.55
20
ŷ=5.94·x-4.36
20
ŷ=-2.73·x+1.43
SAR Determination (%)
MDF Descriptor
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-One-Out
78
inMrpQg
Charge (Q)
Space (geometry)
Q-2
Inversed
r=0.8814; s=0.76;
F (p)=63 (2.84·10-7)
rcv-loo=0.8546; scv-loo=0.84;
Fcv-loo (p)=49 (1.65·10-6)
78
ibDRPQg
Charge (Q)
Space (geometry)
Q2
Inversed
r=0.8832; s=0.50;
F (p)=65 (2.50·10-7)
rcv-loo=0.8611; scv-loo=0.54;
Fcv-loo (p) = 51 (1.13·10-6)
79
AmDROQg
Charge (Q)
Space (geometry)
Q
Proportional
r=0.8901; s=0.24;
F (p)=69 (1.48·10-7)
rcv-loo=0.8545; scv-loo=0.28;
Fcv-loo (p) = 48 (1.78·10-6)
Hydrophobicity on the Manavalan & Ponnuswamy, the Fauchere et al., and the Rao & Argos
scales proved to be of geometrical nature and linearly depended on partial charge. All the
above MDF SAR models presented a weak coefficient of determination (the values were higher
than 75%). At this value, there is an important linear relationship between the molecular
descriptor and the hydrophobic or hydrophilic character.
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-One-Out
20
ŷ=1.74·x+0.86
81
inMrpQg
Charge (Q)
Space (geometry)
Q-2
Inversed
r=0.8974; s=0.05;
F (p)=76 (6.76·10-8)
rcv-loo=0.8744; scv-loo=0.06;
Fcv-loo (p) = 56 (6.37·10-7)
20
ŷ=-3.78·x+5.30
85
IAmrLQg
Charge (Q)
Space (geometry)
Q·d
Identity
r=0.9208; s =0.80;
F (p)=100 (8.69·10-9)
rcv-loo=0.9073; scv-loo=0.68;
Fcv-loo (p) = 84 (3.48·10-8)
20
ŷ=1.75·x+0.86
90
inMrpQg
Charge (Q)
Space (geometry)
Q2·d-3
Inversed
r=0.8974; s=0.05;
F (p)=74 (8.21·10-8)
rcv-loo=0.8744; scv-loo=0.06;
Fcv-loo (p) = 58 (4.73·10-7)
All three models revealed that the hydrophobic or hydrophilic character was of geometrical
nature and depended on partial charge. The determination was fairly good in these models
(greater than 80%).
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-One-Out
20
ŷ=-11.96·x-29.73
82
iBDMkEt
Electronegativity (E)
Bonds (topology)
Q-2·d-1
Inversed
r=0.9047; s=1.07;
F (p)=81 (4.40·10-8)
rcv-loo=0.8819; scv-loo=1.18;
Fcv-loo (p) = 63 (2.85·10-7)
20
ŷ=-753.09·x+ 1.85
83
INPrWQg
Charge (Q)
Space (geometry)
Q2·d-1
Logarithmic
r=0.9116; s=2.07;
F (p)=89 (2.26·10-8)
rcv-loo=0.8731; scv-loo=2.56;
Fcv-loo (p) = 51 (1.13·10-6)
20
ŷ=-0.92·x+ 1.68
83
IAMdKQg
Charge (Q)
Space (geometry)
Q2·d
Logarithmic
r=0.9128; s=0.42;
F (p)=90 (2.02·10-8)
rcv-loo=0.8935; scv-loo=0.46;
Fcv-loo (p) = 70 (1.31·10-7)
The hydrophobicity on the Urry scale proved to be of topological nature and linearly dependent
on the atomic electronegativity of the standard amino acids studied. The hydrophobicity on the
Engelman et al., and on the Eisenberg et al. scales proved to be of geometrical nature and
directly dependent on the partial charge. The determination was considered rather good.
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor(s)
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-One-Out
20
ŷ=-2.16·x+4.64
84
lbmdKQg
Charge (Q)
Space (geometry)
Q2·d
Logarithmic
r=0.9182; s=0.52;
F (p)=97 (1.15·10-8)
rcv-loo=0.8984; scv-loo=0.58;
Fcv-loo (p) = 75 (7.94·10-8)
20
ŷ=817.95·x+81.72
85
inMrpQg
Charge (Q)
Space (geometry)
Q-2
Inversed
r=0.9232; s=20.73;
F (p)=104 (6.69·10-9)
rcv-loo=0.9082; scv-loo=22.58;
Fcv-loo (p) = 85 (3.16·10-8)
20
ŷ=7.18·x-0.41
85
AmDROQg
Charge (Q)
Space (geometry)
Q
Proportional
r=0.9238; s=0.32;
F (p)=105 (6.24·10-9)
rcv-loo=0.9018; scv-loo=0.58;
Fcv-loo (p) = 78 (6.01·10-8)
The hydrophobicity on the Cowan et al. scale is of geometrical nature and depends on charge.
The same is valid for the model with fifteen amino acids. This observation is also true for the
hydrophobicity on the Hessa et al. scale [18], the determination being lower than in the model
obtained on the sample of fifteen amino acids. All models revealed that the hydrophobic or
hydrophilic character was of geometrical nature and depended on the partial charge.
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor(s)
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity/Property Scale
Model Statistics
Cross-Validation Leave-One-Out
20
ŷ=-0.20·x+1.36
85
iIPmLQt
Charge (Q)
Bonds (topology)
Q·d
Inversed
r=0.9252; s=0.36;
F (p)=107 (5.30·10-9)
rcv-loo=0.9003; scv-loo=0.42;
Fcv-loo (p) = 75 (8.02·10-8)
20
ŷ=1.85·x+11.05
86
lfPROQg
Charge (Q)
Space (geometry)
Q
Logarithmic
r=0.9259; s=2.46;
F (p)=108 (4.88·10-9)
rcv-loo=0.8935; scv-loo=2.97;
Fcv-loo (p) = 69 (4.91·10-8)
20
ŷ=19.17·x-7.60
87
IiDRLQt
Charge (Q)
Bonds (topology)
d·Q
Identity
r=0.9328; s=1.11;
F (p)=120 (2.10·10-9)
rcv-loo=0.9226; scv-loo=1.18;
Fcv-loo (p) = 103 (7.25·10-9)
Hydrophobicity is of geometrical nature and depends on charge. In these models, the
determination is slightly better compared with the above models in the sample of twenty
standard amino acids.
Twenty Standard Amino Acids – Hydrophobicity [Bold & Italic]
Sample size
MDF SAR Equation
SAR Determination (%)
MDF Descriptor(s)
Dominant Atomic Property
Interaction Via
Interaction Model
Structure on Activity Scale
Model Statistics
Cross-Validation Leave-OneOut
20
ŷ=-0.96·x+0.86
88
lAmrLQg
Charge (Q)
Space (geometry)
d·√Q
Proportional
r=0.9376; s=0.12;F (p)=131 (1.09·10-9)
rcv-loo=0.9263; scv-loo=0.13;
Fcv-loo (p)=109 (4.73·10-9)
19 (- Proline)
ŷ=843.88·x+86.05
90
inMrpQg
Charge (Q)
Space (geometry)
Q-2
Inversed
r=0.9504; s=16.49; F (p)=159 (4.77·10-10)
rcv-loo=0.9380; scv-loo=18.37;
Fcv-loo (p)=125 (3.00·10-9)
The best determination on the sample of twenty amino acids was obtained for the Black et al.
scale. On the Monera et al. scale the determination was better but the sample was of nineteen
amino acids (Proline was the amino acid excluded from the generation of molecular
descriptors).
As an overall conclusion, the hydrophobicity of amino acids is of geometrical nature and
depends on partial charge.
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